Name: _______________________________________ Date: _______________________ Period: _____
ID: R
Algebra II: Mid-Chapter 5 Review (5.1-5.4)
Short Answer
1. Classify the polynomial by degree and number
4. Classify the polynomial by degree and number
of terms.
of terms.
−3
2x + 7
Degree: __________________
Degree: __________________
# of Terms: __________________
# of Terms: __________________
2. Classify the polynomial by degree and number
5. Classify the polynomial by degree and number
of terms.
of terms.
2x 2 − 7x 4 + 9x − 5
6x − 4 + 3x 5
Degree: __________________
Degree: __________________
# of Terms: __________________
# of Terms: __________________
3. Classify the polynomial by degree and number
6. Perform the operation and simplify.
of terms.
7x
(3x + 2) − (x − 4)
3
Degree: __________________
# of Terms: __________________
7. Perform the operation and simplify.
6x 7 + 9x 7
1
8. Perform the operation and simplify.
11. Perform the operation and simplify.
ÁÊÁ 3x 2 + 2x + 8 ˜ˆ˜ − (2x + 9)
Ë
¯
(3x + 5)(3x − 5)
9. Perform the operation and simplify.
12. Perform the operation and simplify.
ÁÊÁ −4x 3 ˜ˆ˜ ÁÊÁ −9x 7 ˜ˆ˜
Ë
¯Ë
¯
(3x − 5)
10. Perform the operation and simplify.
2
13. Perform the operation and simplify.
Ê
ˆ
7x 3 ÁÁ −2x 4 − 9x ˜˜
Ë
¯
Ê
ˆ
(2x − 7) ÁÁ −3x 2 − 11x − 4 ˜˜
Ë
¯
2
14. Find the zeros of the graph below.
16. Find the factors of the graph below.
Factors: _________, _________,
Zeros: _________, _________, _________
_________, _________
17. State the roots of the graph below. State the
multiplicity if it is more than 1.
15. State the end behavior of the graph below.
Label the end behavior as UP or DOWN.
Roots: ___________, ____________
Left: ____________
Right: ___________
3
18. State the relative maximum value and relative
20. State the x-intercept(s) and y-intercept of the
minimum value of the graph below.
graph below.
Relative Maximum: _________________
x-int: ______________________________
Relative Minimum: _________________
y-int: ______________________________
19. State the domain and range of the graph below.
21. Use the graph below to state the intervals over
which the function is increasing, decreasing, or
constant.
Domain: ___________________________
Increasing: ____________________
Range: ____________________________
Decreasing: ___________________
Constant: _____________________
4
22. Write a polynomial of least degree with roots 0,
3, and −4.
24. Find the real or imaginary solutions of the
equation.
(x + 2) 2 (x + 6)(x − 4) = 0
23. Find the real or imaginary solutions of the
equation.
(x − 2)(x − 5)(4x + 3) = 0
25. Find the real or imaginary solutions of the
equation. (Hint: Factor out a GCF if possible,
then use factoring, completing the square or the
quadratic formula to solve, if necessary).
3x 2 + 6x − 105 = 0
5
26. Find the real or imaginary solutions of the
28. Find the real or imaginary solutions of the
equation. (Hint: Factor out a GCF if possible,
then use factoring, completing the square or the
quadratic formula to solve, if necessary).
equation. (Hint: Factor out a GCF and then
use factoring, completing the square or the
quadratic formula to solve, if necessary).
x 4 − 121x 2 = 0
x 3 − 10x 2 + 24x = 0
27. Find the real or imaginary solutions of the
29. Find the real or imaginary solutions of the
equation. (Hint: Factor out a GCF if possible,
then use factoring, completing the square or the
quadratic formula to solve, if necessary).
equation. (Hint: Factor out a GCF if possible,
then use factoring, completing the square or the
quadratic formula to solve, if necessary).
4x 3 + x 2 − 11x = 0
x 4 − 5x 3 − 36x 2 = 0
6
32. Divide. Write the quotient along with the
30. Is x + 5 a factor of 3x 3 + 8x 2 + 5x − 7? Show work
to justify your answer.
remainder as a fraction.
(x 3 − 4x 2 − 7x − 38) ÷ (x + 8)
33. Simplify:
31. Given P(x) = 3x 3 − 4x 2 + 2x + 6 , find P(−3) . Show
work to justify your answer.
x 3 + 343
x+7
7